There was also a scene at the end of the script where Worf and Geordi are cleaning out Data's quarters, and Geordi discovers that Data didn't have his emotions chip in (the implication apparently being that, in being able to make his self-sacrifice, Data had transcended his core programming). This scene was filmed, but like many of the character building moments it was removed in the final edit.
IMO this is the kind of thing they neeeded to work on to make Data's death feel more significant. This, and remove that final scene where Picard "discovers" that B4 is beginning to recover Data's memories. Draw and line under Data's death (instead of hinting that he isn't dead after all), and it becomes a powerful and defining moment, instead of simply being a "huh, I guess he'll be back in the next movie" one.